Question

Find the probability that a randomly selected person from the sample is female or prefers chocolate.

Answer 1

To find the probability that a randomly selected person from the sample is female or prefers chocolate, we need to find the probabilities of being female and preferring chocolate individually and then add them together.

Step-by-step explanation:

To find the probability that a randomly selected person from the sample is female or prefers chocolate, we first need to find the probability of each event individually and then add them together.

Let's say the probability of being female is P(F) and the probability of preferring chocolate is P(C).

1. To find P(F), we need to know the total number of females in the sample and divide it by the total number of people in the sample.

2. To find P(C), we need to know the total number of people who prefer chocolate and divide it by the total number of people in the sample.

3. To find P(F AND C), we need to know the total number of people who are both female and prefer chocolate and divide it by the total number of people in the sample.

4. Finally, to find P(F OR C), we can use the formula: P(F OR C) = P(F) + P(C) - P(F AND C).

Answer 2

The probability that a randomly selected person from this sample is female OR prefers chocolate is 40/50, which is 4/5 or 80%.

Based on the information in the table, No, the events "female" and "prefers chocolate" are not mutually exclusive.

Here's why:

Mutually exclusive events cannot happen at the same time. In this case, a person can be both female and prefer chocolate. The table shows that 15 females prefer chocolate, which means both events can occur simultaneously for the same individuals.

Therefore, the answer to the first question is No.

Now, let's find the probability that a randomly selected person from this sample is female OR prefers chocolate. This can be calculated by adding the probabilities of being female and preferring chocolate, since those events are not mutually exclusive.

Here's how to calculate the probability:

P(female OR prefers chocolate) = P(female) + P(prefers chocolate) - P(both female and prefers chocolate)

From the table, we can see:

P(female) = 22/50 (since 22 out of 50 people are female)

P(prefers chocolate) = 33/50 (since 33 out of 50 people prefer chocolate)

P(both female and prefers chocolate) = 15/50 (since 15 females prefer chocolate)

Plugging these values into the formula:

P(female OR prefers chocolate) = 22/50 + 33/50 - 15/50

P(female OR prefers chocolate) = 40/50

Complete the question:

Fifty people were surveyed about their preference between chocolate and vanilla cake. The following two-way table displays data for the sample of people who responded to the survey. In this sample, are the events "female" and 'prefers chocolate" mutually exclusive? Choose 1 answer: A Yes No Find the probability that a randomly selected person from this sample is female OR prefers chocolate. P (female OR prefers chocolate)